ellipap

Elliptic analog lowpass filter prototype

Syntax

[z,p,k] = ellipap(n,Rp,Rs)

Description

[z,p,k] = ellipap(n,Rp,Rs) returns
the zeros, poles, and gain of an order n elliptic
analog lowpass filter prototype, with Rp dB
of ripple in the passband, and a stopband Rs dB down from the peak value in the passband. The zeros
and poles are returned in length n column vectors z and p and
the gain in scalar k. If n is
odd, z is length n - 1. The transfer function in factored
zero-pole form is

H(s)=z(s)p(s)=k(s−z1)(s−z2)…(s−zN)(s−p1)(s−p2)…(s−pM)

Elliptic filters offer steeper
rolloff characteristics than Butterworth and Chebyshev filters, but
they are equiripple in both the passband and the stopband. Of the
four classical filter types, elliptic filters usually meet a given
set of filter performance specifications with the lowest filter order.

ellipap sets the passband edge angular
frequency ω0 of the elliptic filter to
1 for a normalized result. The passband edge angular frequency is
the frequency at which the passband ends and the filter has a magnitude
response of 10-Rp/20.